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'fragments/reports', 'Philosophy of Language' and 'On Formally Undecidable Propositions'
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8 ideas
5. Theory of Logic / B. Logical Consequence / 5. Modus Ponens
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8078
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Modus ponens is one of five inference rules identified by the Stoics [Chrysippus, by Devlin]
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5. Theory of Logic / D. Assumptions for Logic / 2. Excluded Middle
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6023
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Every proposition is either true or false [Chrysippus, by Cicero]
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5. Theory of Logic / F. Referring in Logic / 1. Naming / c. Names as referential
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7306
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If the only property of a name was its reference, we couldn't explain bearerless names [Miller,A]
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5. Theory of Logic / K. Features of Logics / 1. Axiomatisation
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17886
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The limitations of axiomatisation were revealed by the incompleteness theorems [Gödel, by Koellner]
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5. Theory of Logic / K. Features of Logics / 2. Consistency
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10071
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Second Incompleteness: nice theories can't prove their own consistency [Gödel, by Smith,P]
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5. Theory of Logic / K. Features of Logics / 3. Soundness
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19123
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If soundness can't be proved internally, 'reflection principles' can be added to assert soundness [Gödel, by Halbach/Leigh]
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5. Theory of Logic / K. Features of Logics / 5. Incompleteness
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10621
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Gödel's First Theorem sabotages logicism, and the Second sabotages Hilbert's Programme [Smith,P on Gödel]
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17888
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The undecidable sentence can be decided at a 'higher' level in the system [Gödel]
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